The \(\mathsf {CONGEST}\)  model: Algorithms for finding larger cliques in the \(\mathsf {CONGEST}\)  model, as in the case of triangles, are also based on the conductance decomposition algorithms of Chang, Pettie, and Zhang [1]} and of Chang and Saranurak [2]}. The first sublinear algorithms for larger cliques in \(\mathsf {CONGEST}\)  are due to Eden, Fiat, Fischer, Kuhn, and Oshman [3]}. They show that 4-cliques can be listed in \(\tilde{O}(n^{5/6+o(1)})\)  rounds and that 5-cliques can be listed in \(\tilde{O}(n^{73/75+o(1)})\)  rounds, w.h.p. These listing algorithms are more involved compared with the triangle listing algorithm, due to the need to handle, for example, a 4-clique with one edge within a certain component and another edge within a different component, which imposes a complex challenge that becomes even worse as \(p\)  grows.
